Lesson video

Hi there, thank you for joining me.

My name is Ms. Jeremy, and today's math lesson is focused on solving multi-step addition and subtraction problems. So find yourself a nice quiet space ready for learning, and then press play when you're ready to begin the lesson.

Let's begin by looking at the lesson agenda for today.

We're going to start with a warm up which will be a recap of using the column method.

We are then going to look at new subtraction strategies before applying some of these strategies to word problems. And in your developed learning, we'll continue with our independent practise and a quiz at the end of the lesson.

For today's lesson, you will need a pencil and some paper, and a nice quiet space.

So find these resources, press pause now and when you're ready to begin, press play to start your lesson.

So let's start with a warm up.

Let's have a little recap of using the column method.

Our question here says, in which columns will regrouping be required? How do you know? So we've got an equation here which is a three step equation, it's got three parts.

And we want to know which columns will require regrouping.

Have a look at those columns.

We've got the digits in ones, tens, hundreds, and thousands columns, which of those columns will require regrouping and how do you know? Will give you five seconds to see if you can have a guess.

Okay, so let's have a look at it together.

Well, I know that I'm going to need to regroup in an addition equation whenever my number goes above nine.

So if I can see that it's likely my numbers will go above nine in one particular column, it's likely that regrouping will occur.

So looking at my ones column first of all, well I can see I'm initially having seven plus six.

Straight away, I know that's going to go over that boundary of the nine and take me into regrouping territory.

So I know that's going to need regrouping.

For the tens column, that looks like it's going to be below nine.

So we'll have a look at that, it might be that it's above depending on how we regroup our ones, but at the moment it's looking like it's below.

And for our hundreds, we can see there that we've got 200 plus 500 plus 300, and that looks like we are going to require some regrouping as well.

And finally, in the thousands column, it looks like regrouping might be required.

So it's always useful to have a scan of your columns just to determine if regrouping will be necessary, so you're prepared for that.

Let's have a go at calculating the answer to our question.

So we'll start with our ones column.

Let's see if we can work through using our ones.

So seven ones plus six ones plus one one.

Well I'm going to start my seven plus my six.

I know that seven plus seven, doubling seven is 14.

So seven plus six must be 13 adding on the one, that's 14 ones.

So I do need to regroup here.

I need to put four in the ones column, and regroup my one 10 at the tens column.

So now I've got my tens.

I've got one 10 plus one 10 plus four tens plus two tens.

How many tens do I have now? Five seconds.

Okay, so I can see that if I have my four tens plus my two tens, that's six tens plus another two tens, that's equal to eight tens or 80.

So I'm going to put eight tens in column here.

Now looking at my hundreds, I've got 200 plus 500 plus 300.

How many hundreds do I have? So you should see that I have 10 hundreds, which is equivalent to 1000.

So I'm not going to have anything in my hundreds column anymore because I'm going to regroup those 10 hundreds or one 1000 up to the thousands columns.

And now let's look at our thousands.

Which way or what is the best way to add together these thousands, using the commutative rule, we can choose any of those numbers to add in whichever order we prefer.

How would you decide add those digits together.

So for me, what I would do is I would start with my number bonds to 10.

I can see that six plus four gives me 10.

So 6,000 plus 4,000 gives me 10,000.

Then I'm going to add my 8,000 plus my 1000, which is equal to 9,000.

So 10,000 plus 9,000 is equal to 19,000.

So I'm going to keep 9,000 here and regroup my one 10,000 into the 10 thousands column there.

So my answer is 19,084.

And then in this blue box, it says, how will we know whether our answer is accurate? So what could we do to double check this? I'm going to give you a couple of seconds to see if you can come up with some strategies that would help us double check this.

So for me, there are three things that we could do to double check this.

The first one, we should have really done it in the beginning, which was to estimate the answer.

If we were round each of those numbers to the nearest multiple of 1000, we could have estimated what a rough answer would have been.

And that would have helped us work out with whether our answer is accurate or not.

Something that we could do now that we've calculated the answer is use the inverse method.

So I could go back and I could actually subtract all of those numbers from my original answer, to see whether I get back to my starting point, to see whether I get back to zero.

And finally, what I could also do is use a different method, a different addition method, for example, partitioning or counting on, and I could use that to double check my answer.

So there's lots of different ways we could check to see whether our answer is correct.

So moving on, adding on a little bit for today's learning, we're going to look at some subtraction strategies.

And we're looking at questions that involve lots and lots of regrouping where the column method might actually not be the most appropriate method to use because of the amount of regrouping required.

So, let's have a look at this equation on the screen.

It says 10,000 minus 6,320, and asks us which strategies we could to solve this.

I'm going to introduce you to two new strategies that you might use in the condition that you've got lots of regrouping to do, like the case that we have on the screen here.

The first strategy is called the counting back strategy and involves counting backwards from 10,000 using a number line strategy, using a number line method.

Let me show you how it works.

We're going to start with 10,000 at this end of our number line because we're subtracting and 10,000 is a whole.

So I'm going to put 10,000 at the very end here, and we're going to count backwards 6,320.

We're going to try and do this as proportionately as possible, so my jumps will reflect how big a jump, how big a subtraction we're actually doing.

So I'm going to partition this out.

I'm going to start by subtracting 6,000.

So that's part of my subtraction, now I'm going to subtract 6,000 just there.

Now using my number bonds, I know that 10 minus six is equal to four.

10,000 minus 6,000 is equal to 4,000.

So I've subtracted 6,000.

Now I'm going to try and subtract 300.

So I'm going to do a bit of a smaller jump this time.

I'm subtracting 300 now and 4,000 subtract 300.

Well I know that, 1000 subtract 300 is equal to 700.

The 4000 subtract 300 must be equal to 3,700.

And then very finally, I'm going to do a little jump.

In fact, that should be a smaller jump there, a little jump of 20.

And typically it would take you to the end of the number line here.

So, but you can demonstrate a slightly earlier finish if you need to.

So 3,700 minus 20.

Well, if I was calculating 700 minus 20, I'd get to 680.

So 3,700 minus 20 is 3,680.

So that's called the counting back strategy.

We start with a whole and we partition our parts and subtract those different components of our parts.

The other strategy we have is called the counting on strategy.

I need to change my pen colour so you can see really clearly the difference between this one.

So in red, let's use the counting on strategy.

So this time we start with one of our parts because we're effectively finding the difference between 6,320 and 10,000, I'm going to start with 6,320, and I'm going to end with 10,000.

And what I'm going to do is find the difference between those two values by counting on.

So, I'm going to start by doing a jump to my next kind of large number or my next kind of easy number to work with.

So I'm going to see if I can jump from 6,320 to 6,400.

What do I have to add to 6,320 to get to 6,400? I need to add 80.

So this is adding on 80 here.

Now, to get from 6,400, I'm going to try and jump to get to 7,000.

So slightly bigger jump this time, I'm jumping to get to 7,000 this time.

What do I have to add to 6,400 to get to 7,000? Well, what would I have to add to 400 to get to 1000 or add to 40 to get to 100.

I'm looking at my number bonds here, my know number facts to help me.

So I know that I'd add six to four to get to 10, 60 to 40 to get to 100, and then 600 to 400 to get to 1000.

So I'm adding here 600 to get to 7,000.

And then from 7,000, all the way to 10,000, well I know to get from seven to 10, I add three.

So from 7,000 to 10,000, I'm adding 3000.

And you can see here, we get exactly the same answer as we did previously.

We get 3000 if we add the differences, 680.

So either way, we get the same answer.

I counted backwards initially, where I started with my whole and subtracted my parts.

And then the second example that I started my parts and an added on until I got to my whole.

Either way, you get to 3,680, which is our answer, Which of those methods do you prefer? Do you prefer starting with your whole and counting backwards? Or do you prefer starting with your part and counting onwards.

Have a think now about which method you think is best? So let's have a practise of this.

what I'd like you to do is, have a look at the equation on the screen, it says 10,000 minus 7,890.

I would like you to use both the counting back and the counting on strategies to solve this equation.

So you need to draw yourself a number line for the counting back strategy and then another one for the counting on strategy, and check to see whether you get the same answer each time.

Pause the video to complete your task and then resume it once you're finished.

Okay, how did you get on it? Let's have a look how these might've looked for you.

So in this case here, we've got the counting back strategy.

We started at 7,000, at 10,000 sorry, subtracted 7,000, subtracted 800 and then subtracted 90.

And then in the second one here, we've got the counting on strategy starting with 7,890 counting on to 7,900, 8,000 and then 10,000.

And we haven't got the final answer in here yet.

We're going to add that in as we go.

So let's see if we can do this.

So let's start with the first one, the counting back strategy.

I'm going to start with 10,000 and subtract 7,000.

You should have found that gave you 3000.

And then we're going to subtract 800, and you should have found that gave you 2,200.

And then you should have attracted 90, which should have given you 2,110.

Looking at the second one, just to double check.

We're starting with 7,890, and I have to add on 10 to get to 7,900.

Then I'm adding on 100 to get to 8,000.

And then I'm adding on 2000 here to get to 10,000.

And looking at the difference here, I've got 2,110 and 2,110.

So for both of those different strategies, you should have got the same answer.

So let's applies some of these strategies to a real problem.

Have a look at the table on the left hand side of your screen.

This table, has recorded the number of steps that I have walked from Monday all the way through to Sunday using what we call a pedometer.

A pedometer is a way of measuring the number of steps you use, or the number of steps you take.

Now I have a daily step target, 10,000 steps.

How far was I from my target on Wednesday? So you can see on Wednesday, I didn't reach 10,000 steps.

I didn't reach that 10,000 steps on Monday, Tuesday, and Thursday, either.

But on Wednesday, I reached 8,005 steps.

And I want to know, how far was I from my target on Wednesday.

So, I want you to decide whether we should use the counting on strategy or the counting back strategy.

Which one do you think would be best in this case.

Decide in the next couple of seconds.

So either is absolutely fine in this case.

However, I think I'm going to use the counting back strategy.

The reason being, I can see that I'll only need to partition this number into 8,000 and 5, which is fairly straightforward.

And that I think will be a more efficient method for me to use.

So I'm going to use the counting back strategy to support me here.

So starting with 10,000 at the end, that's my whole.

And I'm going to see whether I can count backwards, 8,005.

So I'm doing a huge big jump first of all.

I'm subtracting 8,000 first of all.

And I know that 10,000 subtract 8,000 is equal to 2000.

And then I've got to subtract five, that little bit of five there.

And so I know that 2000 subtract five is equal to 1,995.

So, at the moment you can say that on Wednesday, I was 1,995 steps away from my target.

If you chose the counting on strategy instead, why not pause the video now, and calculate the answer to this using your counting on strategy, to see whether it matches my counting back strategy.

So let's look at this next step of the problem.

It says my target has now increased to 15,000 steps, was 10,000, it's now gone up 5,000.

It's 15,000.

How far was I away from my target on Monday? I would like you to use both the counting back and the counting on strategy to solve this problem.

You can see there's two number lines there.

So I'd like you to draw yourself two number lines, use the counting back strategy then the counting on strategy to solve this.

Pause the video to complete your task and resume it once you're finished.

So let's go through the answers and see how you go on.

So remembering that we're going to use our counting back strategy first, and that means I'm going to place my whole at the end of my number line, so am placing 15,000 just here, and I'm going to come back with 7,890.

So let me start with that big jump.

Let's start with counting backwards 7,000.

So I'm going to do a big jump backwards and I'm subtracting 7,000 from 15,000.

Let me use my know number facts here.

I know that 15 minus seven is equal to eight.

So 15,000 minus 7,000 must be equal to 8,000.

So now I've subtracted my 7,000, let me subtract my 800.

So I'm subtracting 800 here.

Now, I know that 1000 minus 800 is equal to 200, so 8,000 minus 800 must be equal to 7,200, and then I'm subtracting my 90.

So 7,200 minus 90.

Well, 200 minus 90 would be equal to 110, 7,200 minus 90 is equal to 7,110.

So that's what our final answer is there 7,110.

Let's double check it using the counting on strategy.

This time I start with my parts, I'm going to start with 7,890, and I need to count all the way up until I reach 15,000, which is my whole.

Let me do a little jump of adding 110 first of all, to get me all the way up to 7,900.

Then a jump of 100 to get me to 8,000 and then a big jump of how much do I have to add to 8,000 to get to 15,000.

I have to add 7,000.

So there we have it 7,110.

That is the difference between the number of steps I reached on Monday and my actual target, which is 15,000 steps.

How did you get on with those? Did you manage to get the final answer? So lets practise applying some of these strategies to more complex problems. Have look at the little map you can see on your screen here.

This is a map of my town and you can see the dotted lines in between each location in the town represent my walking distance.

So the numbers that you can see, are the number of steps it takes to reach those destinations.

For example, to walk from my home into the town centre, I would walk 4,215 steps.

The question I have for you is what is the best route or how many different possible routes are there that I could take that would help me reach my goal of 15,000 steps? Which of those routes would I need to take in order to reach that number of steps? And I've got lots of options here.

I could walk from my home to the park, then round the park, then to town, then to the river then back home again.

I could walk from my home to town to back home again, back to town again.

I could walk from my home to the park, to town, back home.

Lots of different options here, but I want you to know which options will help me reach that target count of 15,000 steps.

And we're going to use an estimate and calculate type of strategy to help us here.

So what we're going to do, is have a guess at which route might be best estimate tell me steps that would give me, and then look at some other possibilities of routes as well.

So, let's imagine that I decided that my first route is going to be from my home to the river, to town, back home again.

Let's look at those numbers that I will be working with in that instance.

So, what I'm going to do is use an estimation strategy where I'm going to round each of those numbers.

And I think I'm going around those numbers, the nearest multiple of 100.

When I have them together, I'm going to see how close I am to 15,000.

If I'm still really far off, I need to think of a different way to reach my target.

So, let's look at the first number 1,320.

What is that rounded to the nearest multiple of 100? It is 1,300.

Now looking at 2,350, that rounded to the nearest multiple of 100 is 2,400 and finally 4,215 rounded to the nearest multiple of 100 is 4,200.

So using partitioning, let me add these numbers together and see how close I get to 15,000.

I'm going to start by adding all of my thousands together.

So I've got 1000 plus 4,000 plus 2000.

Three seconds to work out what that would be.

So you should have got 7,000.

So that would equal 7,000.

And then let's add all my hundreds.

So I've got 300, plus 200 plus 400.

What would that be equal to? Okay so that would be equal 400 plus 300 is equal to 700 plus 200 is equal to 900.

So my estimated answer, and it would be lower because all of those calculations would be rounded down.

But my estimated answer is about 7,900 steps.

That is too few, in fact, that is pretty much halfway to where I need to be.

So, I need to think of a different route that I could take in order to reach my 15,000 steps.

Which route do you think I should take? Have a think about the best possible route that we could take in order to reach 15,000 steps.

So rubbing out my markings, let's have another look.

Let's see if we can try a different route.

I am going to try this time, walking from the home to my park, all the way around the park, then to town, then back home again.

We're going to estimate to see whether that would be a likely answer or likely strategy to reach 15,000 steps.

So rounding my first number to the nearest multiple of 100, 2,435 is rounded to 2,400.

And then I've got 5,345, which is rounded to 5,300 and then 3140, 3100.

And finally 4,215 is 4,200.

So, let's see if this is any better.

Adding together my thousands first of all, 5000 plus 3000 plus 4,000 plus 2000.

Three seconds.

Okay, so I'm adding my 5,000 plus 3000 first, that's equal to 8,000, plus 4,000 is equal to 12,000, plus 2000 is equal to 14,000.

Total 14000.

Now let's add together my hundreds.

Let's add 400 plus 200, that's equal to 600 plus 100 which is equal to 700, plus 300 which is equal to 1000.

So, 14,000 plus 1000 is equal to 15,000.

That, as my estimate looks a lot healthier than my previous calculation.

So that looks like it might be possible.

I am going to need to calculate the answer in order to work out if it will actually.

And that's where your strategies come in.

So I could use the column method for this, the partitioning method, or the counting on strategy if I wanted to to add together those numbers.

But according to my estimate, we're in a good position for that to reach my target of 15,000 steps.

All right, this is what I want you to do for your independent task.

We've already started looking at this together, but I would like you to look at this map.

It's a slightly extended map this time, because I've also got my journey to the supermarket there added in, I want you to find me as many routes as possible, and there is more than, they are more than one, there are several routes in this case, more than one route.

I want you to find as many as possible that would help me reach my target amount of 15,000 steps.

I'd like you to make sure you're estimating before you're calculating.

There's no point setting out a lovely column method with four different numbers that you're adding together, if you're going to be way, way way from that crucial 15,000 steps.

So that's why estimating is really important.

So how many different routes can you find that is going to give me that total amount of 15,000 steps? Create your estimations, write down your different routes and calculate using either the column method or another one of the addition methods that we have looked at.

You might even want to use the counting back strategy, where you count backwards, all of the different amounts from 15,000 to see whether you can get to zero.

Any of those strategies is absolutely fine to use.

Which strategies will you use today to find me those different routes? Pause the video to complete your task and resume it once you're finished.

I hope you managed to find some really lovely roots for me.

If you'd like to, please ask your parent or carer to share your work on Twitter today tagging @OakNational and #LearnwithOak.

It will be really lovely to see some of those routes that you've plotted out, and to see how you've managed to work out, whether they reach that magic number of 15,000 steps.

Now it's time to complete your quiz.

Thank you for joining me for your math lesson today.

It's been brilliant to have you.

Do come and join us for some more maths again soon.

Bye bye.